Benders Decomposition for the Profit Maximizing Capacitated Hub Location Problem with Multiple Demand Classes

Gita Taherkhani · Sibel A. Alumur · Mojtaba Hosseini

75 citations0/0 files storedTransportation Science

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Facility Location and Emergency Management Complexity and Algorithms in Graphs Vehicle Routing Optimization Methods

Abstract

This paper models the profit maximizing capacitated hub location problem with multiple demand classes to determine an optimal hub network structure that allocates available capacities of hubs to satisfy demand for commodities from different market segments. A strong deterministic formulation of the problem is presented, and a Benders reformulation is described to optimally solve large-size instances of the problem. A new two-phase methodology is developed to decompose the Benders subproblem, and two effective separation routines are derived to strengthen the Benders optimality cuts. The algorithm is enhanced by the integration of improved variable-fixing techniques. The deterministic model is further extended by considering uncertainty associated with the demand to develop a two-stage stochastic program. To solve the stochastic version, a Monte Carlo simulation–based algorithm is developed that integrates a sample average approximation scheme with the proposed Benders decomposition algorithm. Novel acceleration techniques are presented to improve the convergence of the algorithm proposed for the stochastic version. The efficiency and robustness of the algorithms are evaluated through extensive computational experiments. Computational results show that large-scale instances with up to 500 nodes and three demand classes can be solved to optimality, and that the proposed separation routines generate cuts that provide significant speedups compared with using Pareto-optimal cuts. The developed two-phase methodology for solving the Benders subproblem as well as the variable-fixing and acceleration techniques can be used to solve other discrete location and network design problems.

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References

2002The Sample Average Approximation Method for Stochastic Discrete Optimization 2004A stochastic programming approach for supply chain network design under uncertainty 1987A quadratic integer program for the location of interacting hub facilities 2007Network hub location problems: The state of the art 1994Integer programming formulations of discrete hub location problems 1999Monte Carlo bounding techniques for determining solution quality in stochastic programs 1986The Location of Interacting Hub Facilities 1996Efficient algorithms for the uncapacitated single allocation p-hub median problem

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2022Facility Location in Logistics and Transportation: An enduring relationship 2021Robust Stochastic Models for Profit-Maximizing Hub Location Problems 2022A mean-CVaR approach to the risk-averse single allocation hub location problem with flow-dependent economies of scale 2022Benders decomposition applied to profit maximizing hub location problem with incomplete hub network 2021Stochastic single allocation hub location problems with balanced utilization of hub capacities

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